Career

Acting and modelling can be done as part time studies even at advanced level. However, it is really good if you are doing it the regular way.
You need to be skilled at communication skills for sure.
Parallel courses are of three types: distance mode, online mode like MOOCs and regular courses.
It depends on what type of course you are doing already.
The parallel courses suggested are:
1 A degree in a popular language that shall be used in your works and place.
2 Content writing and proof reading.
3. Web development and digital marketing.
4. Music and sound mixing basics/audio production.
5. Advertising and public relations management.
6. Director should also learn more about management and business admin.

BA in mass communication is the traditional and the basic degree that takes one to all domains depending on the skilled possessed. For this reason, the learner is advised to take some technical courses/short term trainings and certification, etc.
It provides enhanced language skills and presentation skills via online as well as professional workshops.
Parallel courses must be done with care and proper selection.
Refer the following answers:
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-editing-and-proof-reading-course-for-better-career-prospects-qna-4392895
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-m-sc-in-advertising-management-and-public-relations-for-better-career-qna-4392908
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-direction-for-better-career-prospects-qna-4392881
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-documentary-production-for-better-career-prospects-qna-4392890

BA in mass communication is a traditional course. For this reason, the learner is advised to take some technical courses/short term trainings and certification, etc.
It helps in enhancing language skills and presentation skills via online as well as professional workshops.
There are many similar questions that can help you in understanding the parallel course requirement. While doing MA in media management the career is certainly going towards media management profiles. The managerial profile needs someone with vast understanding of all media profiles and jobs.
I shall not advise equally wide courses as parallel to Post Graduation in advertising. I shall still share that there are MOOCs and some distance learning courses to enhance the advertising management and public relation career.
Refer the following answers:
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-editing-and-proof-reading-course-for-better-career-prospects-qna-4392895
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-m-sc-in-advertising-management-and-public-relations-for-better-career-qna-4392908
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-direction-for-better-career-prospects-qna-4392881
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-documentary-production-for-better-career-prospects-qna-4392890

Screen writing needs language skills as well as creativity. There are lot many language skill courses along with creative writing courses around the world via MOOCs and distance learning. Please choose one.
There are many similar questions that can help you to understand the parallel course required. While doing MA in media management, the career is certainly going towards media management profiles. The managerial profile needs someone with vast understanding of all media profiles and jobs.
I shall still share that there are MOOCs and some distance learning courses to enhance the advertising management and public relations career.
Along with the Master's Degree, an MOOC- Massive Open Online Courses.
Please read the following already available answers:
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-editing-and-proof-reading-course-for-better-career-prospects-qna-4392895
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-m-sc-in-advertising-management-and-public-relations-for-better-career-qna-4392908
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-direction-for-better-career-prospects-qna-4392881
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-documentary-production-for-better-career-prospects-qna-4392890

You can take some MOOCs and short term courses.While doing MA in media management, the career is certainly going towards media management profiles. The managerial profile needs someone with vast understanding of all media profiles and jobs.
I shall not advise equally wide courses as parallel to Post Graduation in advertising. I shall still share that there are MOOCs and some distance learning courses to enhance the advertising management and public relations career.
Parallel courses must be done with care and proper selection.
Along with the Master Degree, some MOOCs- Massive Open Online Courses.
Please read the following answers already available:
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-editing-and-proof-reading-course-for-better-career-prospects-qna-4392895
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-m-sc-in-advertising-management-and-public-relations-for-better-career-qna-4392908
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-direction-for-better-career-prospects-qna-4392881
https://ask.shiksha.com/what-parallel-courses-can-i-pursue-with-a-certificate-in-documentary-production-for-better-career-prospects-qna-4392890